scholarly journals Supercell refinement: a cautionary tale

2019 ◽  
Vol 75 (9) ◽  
pp. 852-860 ◽  
Author(s):  
Jeffrey Lovelace ◽  
Václav Petrícek ◽  
Garib Murshudov ◽  
Gloria E. O. Borgstahl
Keyword(s):  
Lessons Learned ◽  
Protein Crystal ◽  
Cautionary Tale ◽  
Space Groups ◽  
Average Structure ◽  
3D Space ◽  
Refinement Method ◽  
Higher Dimensional ◽  
Model Protein ◽  
Large Unit Cell

Theoretically, crystals with supercells exist at a unique crossroads where they can be considered as either a large unit cell with closely spaced reflections in reciprocal space or a higher dimensional superspace with a modulation that is commensurate with the supercell. In the latter case, the structure would be defined as an average structure with functions representing a modulation to determine the atomic location in 3D space. Here, a model protein structure and simulated diffraction data were used to investigate the possibility of solving a real incommensurately modulated protein crystal using a supercell approximation. In this way, the answer was known and the refinement method could be tested. Firstly, an average structure was solved by using the `main' reflections, which represent the subset of the reflections that belong to the subcell and in general are more intense than the `satellite' reflections. The average structure was then expanded to create a supercell and refined using all of the reflections. Surprisingly, the refined solution did not match the expected solution, even though the statistics were excellent. Interestingly, the corresponding superspace group had multiple 3D daughter supercell space groups as possibilities, and it was one of the alternate daughter space groups that the refinement locked in on. The lessons learned here will be applied to a real incommensurately modulated profilin–actin crystal that has the same superspace group.

Intergrowth polytypoids as modulated structures: a superspace description of the Sr n (Nb,Ti) n O3n + 2 compound series

2001 ◽  
Vol 57 (4) ◽  
pp. 471-484 ◽  
Author(s):  
L. Elcoro ◽  
J. M. Perez-Mato ◽  
R. L. Withers
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Separation Distance ◽  
Space Group ◽  
Space Groups ◽  
Cell Parameters ◽  
Average Structure ◽  
Layer Stacking ◽  
Compound Series ◽  
Three Dimensional Space

A new, unified superspace approach to the structural characterization of the perovskite-related Sr n (Nb,Ti) n O3n + 2 compound series, strontium niobium/titanium oxide, is presented. To a first approximation, the structure of any member of this compound series can be described in terms of the stacking of (110)-bounded perovskite slabs, the number of atomic layers in a single perovskite slab varying systematically with composition. The various composition-dependent layer-stacking sequences can be interpreted in terms of the structural modulation of a common underlying average structure. The average interlayer separation distance is directly related to the average structure periodicity along the layer stacking direction, while an inherent modulation thereof is produced by the presence of different types of layers (particularly vacant layers) along this stacking direction. The fundamental atomic modulation is therefore occupational and can be described by means of crenel (step-like) functions which define occupational atomic domains in the superspace, similarly to what occurs for quasicrystals. While in a standard crystallographic approach, one must describe each structure (in particular the space group and cell parameters) separately for each composition, the proposed superspace model is essentially common to the whole compound series. The superspace symmetry group is unique, while the primary modulation wavevector and the width of some occupation domains vary linearly with composition. For each rational composition, the corresponding conventional three-dimensional space group can be derived from the common superspace group. The resultant possible three-dimensional space groups are in agreement with all the symmetries reported for members of the series. The symmetry-breaking phase transitions with temperature observed in many compounds can be explained in terms of a change in superspace group, again in common for the whole compound series. Inclusion of the incommensurate phases, present in many compounds of the series, lifts the analysis into a five-dimensional superspace. The various four-dimensional superspace groups reported for this incommensurate phase at different compositions are shown to be predictable from a proposed five-dimensional superspace group apparently common to the whole compound series. A comparison with the scarce number of refined structures in this system and the homologous (Nb,Ca)6Ti6O20 compound demonstrates the suitability of the proposed formalism.

Darwin’s molecule

Hemoglobin ◽  
2018 ◽  
pp. 201-232
Author(s):  
Jay F. Storz
Keyword(s):  
Protein Function ◽  
Evolutionary Biology ◽  
Lessons Learned ◽  
Atomic Resolution ◽  
Molecular Adaptation ◽  
Genetic Adaptation ◽  
Biochemical Phenotype ◽  
Causal Connections ◽  
Model Molecule ◽  
Model Protein

Chapter 9 discusses conceptual issues in protein evolution and provides a synthesis of lessons learned from studies of hemoglobin function. Using hemoglobin as a model molecule, we can exploit an unparalleled base of knowledge about structure-function relationships and we can characterize biophysical mechanisms of molecular adaptation at atomic resolution. It is therefore possible to document causal connections between genotype and biochemical phenotype at an unsurpassed level of rigor and detail. Moreover, since the oxygenation properties of hemoglobin provide a direct link between ambient O2 availability and aerobic metabolism, genetically based changes in protein function can be related to ecologically relevant aspects of organismal physiology. We therefore have a solid theoretical framework for making predictions and for interpreting observed associations between biochemical phenotype and fitness-related measures of whole-animal physiological performance. The chapter explores case studies that illustrate how experimental research on functional properties of a well-chosen model protein can be used to address some of the most conceptually expansive questions in evolutionary biology: Is genetic adaptation predictable? Why does evolution follow some pathways rather than others?

scholarly journals Average structures of the disordered β-phase of Pigment Red 170: a single-crystal X-ray diffraction study

2014 ◽  
Vol 70 (2) ◽  
pp. 283-295 ◽  
Author(s):  
Rangana Warshamanage ◽  
Anthony Linden ◽  
Martin U. Schmidt ◽  
Hans-Beat Bürgi
Keyword(s):  
Single Crystal ◽  
Diffuse Scattering ◽  
Bragg Diffraction ◽  
X Ray Diffraction ◽  
Group Setting ◽  
X Ray ◽  
Space Groups ◽  
Average Structure ◽  
Β Phase ◽  
Layer Stacking

The β-phase of the industrially important Pigment Red 170 (β-P.R. 170) has a structure with severe layer stacking disorder. The single-crystal X-ray diffraction pattern consists of a difficult-to-disentangle mix of Bragg diffraction superimposed on rods of diffuse scattering which impede the estimation of accurate Bragg intensities. Two average monoclinic structure models with the same unit-cell dimensions, but different extents of disorder in the layers and different space groups seem plausible, one with the non-conventional space group settingB21/g(No. 14,Z′ = 2) and one inP21/a(No. 14,Z′ = 4). Disordered molecules related by a translation of 0.158bare present in all layers of theB21/gmodel and in every second layer of theP21/amodel. Layer-to-layer contacts are practically the same in both models. According to order–disorder theory, both models are valid superposition structures. Structure-factor calculations show that the pattern of strong and weak Bragg reflections is very similar for the two models.Rfactors indicate that theB21/gmodel is the most economic representation of the average structure. However, given the limitations in data processing, theP21/amodel should not be discarded and further insight sought from a detailed analysis of the experimental diffuse scattering. The difficulties encountered in this analysis raise the question of whether or not the concept of an average structure is applicable in practice to β-P.R. 170.

scholarly journals How to assign a (3 + 1)-dimensional superspace group to an incommensurately modulated biological macromolecular crystal

2017 ◽  
Vol 50 (4) ◽  
pp. 1200-1207 ◽  
Author(s):  
Jason Porta ◽  
Jeff Lovelace ◽  
Gloria E. O. Borgstahl
Keyword(s):  
Crystal Structure ◽  
Three Dimensional ◽  
Real Life ◽  
Group Symmetry ◽  
Protein Crystal ◽  
3D Space ◽  
Structure Solution ◽  
Crystallographic Symmetry ◽  
Aperiodic Crystals ◽  
Periodic Crystal

Periodic crystal diffraction is described using a three-dimensional (3D) unit cell and 3D space-group symmetry. Incommensurately modulated crystals are a subset of aperiodic crystals that need four to six dimensions to describe the observed diffraction pattern, and they have characteristic satellite reflections that are offset from the main reflections. These satellites have a non-integral relationship to the primary lattice and requireqvectors for processing. Incommensurately modulated biological macromolecular crystals have been frequently observed but so far have not been solved. The authors of this article have been spearheading an initiative to determine this type of crystal structure. The first step toward structure solution is to collect the diffraction data making sure that the satellite reflections are well separated from the main reflections. Once collected they can be integrated and then scaled with appropriate software. Then the assignment of the superspace group is needed. The most common form of modulation is in only one extra direction and can be described with a (3 + 1)D superspace group. The (3 + 1)D superspace groups for chemical crystallographers are fully described in Volume C ofInternational Tables for Crystallography. This text includes all types of crystallographic symmetry elements found in small-molecule crystals and can be difficult for structural biologists to understand and apply to their crystals. This article provides an explanation for structural biologists that includes only the subset of biological symmetry elements and demonstrates the application to a real-life example of an incommensurately modulated protein crystal.

scholarly journals Crystal structures of native cytochrome c 6 from Thermosynechococcus elongatus in two different space groups and implications for its oligomerization

2020 ◽  
Vol 76 (9) ◽  
pp. 444-452
Author(s):  
Sven Falke ◽  
Christian Feiler ◽  
Henry Chapman ◽  
Iosifina Sarrou
Keyword(s):  
Crystal Structures ◽  
Redox Activity ◽  
Suitable Model ◽  
X Ray ◽  
Space Groups ◽  
X Ray Crystallography ◽  
Protein Interfaces ◽  
Model Protein ◽  
Laser Sources ◽  
Blue Native

Native cytochrome c 6 was purified from an extract of strain BP-1 of the thermophilic cyanobacterium Thermosynechococcus elongatus. The protein was crystallized, and with only slight modifications of the buffer and vapour-diffusion conditions two different space groups were observed, namely H3 and C2. Both crystal structures were solved; they contained three and six molecules per asymmetric unit and were refined to 1.7 and 2.25 Å resolution, respectively. To date, the structure of native cytochrome c 6 from T. elongatus has only been reported as a monomer using NMR spectroscopy, i.e. without addressing putative oligomerization, and related structures have only previously been solved using X-ray crystallography after recombinant gene overexpression in Escherichia coli. The reported space groups of related cyanobacterial cytochrome c 6 structures differ from those reported here. Interestingly, the protein–protein interfaces that were observed utilizing X-ray crystallography could also explain homo-oligomerization in solution; specifically, trimerization is indicated by infra-red dynamic light scattering and blue native gel electrophoresis in solution. Trimers were also detected by mass spectrometry. Furthermore, there is an indication of post-translational methylation in the crystal structure. Additionally, the possibility of modifying the crystal size and the redox activity in the context of photosynthesis is shaping the investigated cytochrome as a highly suitable model protein for advanced serial crystallography at highly brilliant X-ray free-electron laser sources.

scholarly journals Lessons Learned in Protein Precipitation Using a Membrane Emulsification Technique to Produce Reversible and Uniform Microbeads

Pharmaceutics ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1738
Author(s):  
Sang-Koo Park ◽  
Ga Yeon Noh ◽  
Hyun Woo Yu ◽  
Eun Chae Lee ◽  
Junoh Jeong ◽  
...  
Keyword(s):  
Intravenous Immunoglobulin ◽  
Porous Glass ◽  
Manufacturing Process ◽  
Protein Concentration ◽  
Lessons Learned ◽  
The Other ◽  
Silicone Resin ◽  
Hydrophobic Modification ◽  
Hydrophobically Modified ◽  
Model Protein

The effects of the manufacturing process and the regeneration of Shirasu porous glass (SPG) membranes were investigated on the reproducibility of protein precipitants, termed protein microbeads. Intravenous immunoglobulin (IVIG) was selected as a model protein to produce its microbeads in seven different cases. The results showed that the hydrophobically modified SPG membrane produced finer microbeads than the hydrophilic SPG membrane, but this was inconsistent when using the general regeneration method. Its reproducibility was determined to be mostly dependent on rinsing the SPG membrane prior to the modification and on the protein concentration used for emulsification. The higher concentration could foul and plug the membrane during protein release and thus the membrane must be washed thoroughly before hydrophobic modification. Moreover, the membrane regenerated by silicone resin dissolved in ethanol had better reproducibility than silicone resin dissolved in water. On the other hand, rinsing the protein precipitant with cold ethanol after the emulsification was not favorable and induced protein aggregation. With the addition of trehalose, the purity of the IVIG microbeads was almost the same as before microbeadification. Therefore, the regeneration method, protein concentration, and its stabilizer are key to the success of protein emulsification and precipitation using the SPG membrane.

scholarly journals Dealing with Aperiodic Protein Crystal Structures

2014 ◽  
Vol 70 (a1) ◽  
pp. C778-C778
Author(s):  
Gloria Borgstahl
Keyword(s):  
Three Dimensional ◽  
Protein Crystal ◽  
Periodic Lattice ◽  
X Rays ◽  
Future Directions ◽  
Space Group ◽  
3D Space ◽  
Structure Solution ◽  
Quasi Crystals ◽  
Aperiodic Crystals

Protein crystals can be aperiodic. They will diffract X-rays, and are therefore a crystal, but their diffraction is not periodic. This means that their diffraction pattern cannot be simply be indexed by a typical three-dimensional unit cell and space group. Aperiodic crystals include "quasi-crystals" as well as "modulated" crystals. In the latter case, the modulation can be positional or occupational and these modulations can be incommensurate with the normal periodic lattice [1]. An overview of aperiodic protein crystal diffraction will be presented with examples. The discussion will then focus on the characteristics of incommensurately modulated crystals followed by a more detailed discussion of how to solve these crystals. The following details of structure solution will be presented: (1) data collection perils; (2) specialized diffraction data processing in (3+1)D space using a q-vector [2]; (3) how to get an approximation of the structure in 3D space; (4) the assignment of the (3+1)D space group; and the ultimate (5) crystallographic refinement in superspace[3]. Future directions and needs will be discussed.

Reliability of atomic displacement parameters in protein crystal structures

1999 ◽  
Vol 55 (2) ◽  
pp. 473-478 ◽  
Author(s):  
Oliviero Carugo ◽  
Patrick Argos
Keyword(s):  
Protein Structures ◽  
Atomic Displacement ◽  
Protein Crystal ◽  
Nonlinear Dependence ◽  
Standard Errors ◽  
Unexpected Result ◽  
Protein Chain ◽  
Space Groups ◽  
Structure Determinations ◽  
Atomic Displacement Parameters

Mean standard errors in atomic displacement parameters (ADPs) resulting from protein crystal structure determinations are estimated by comparing the ADPs of protein-chain pairs of identical sequence within the same crystal or within different crystals displaying the same or different space groups. The estimated ADP standard errors increase nearly linearly as the resolution decreases – an unexpected result given the nonlinear dependence of the resolution on the amount of diffraction data. The estimated ADP standard errors are larger for side-chain and solvent-exposed atoms than for main-chain and buried atoms and, surprisingly, are also larger for residues in the helical secondary structure relative to other local backbone conformations. The results allow an estimate of the influence of crystallographic refinement restraints on ADP standard errors. Such corrections should be applied when comparing different protein structures.

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